 Dataplot Vol 2 Vol 1

# Q QUANTILE RANGE

Name:
Q QUANTILE RANGE (LET)
Type:
Let Subcommand
Purpose:
Compute the q quantile range for a variable.
Description:
The q quantile range is defined as:

QQ = X1-q - Xq

where q defines a quantile between 0 and 0.5 and Xq denotes the q-th quantile of the data.

For example, if q = 0.20, then the q quantile range is the difference between the 80th and 20th quantiles of the data. The interquartile range is a special case of the q quantile range with q = 0.25.

The q quantile range is used as a robust measure of scale.

Syntax:
LET <par> = Q QUANTILE RANGE <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<par> is a parameter where the computed q quantile range is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = Q QUANTILE RANGE Y1
LET A = Q QUANTILE RANGE Y1 SUBSET TAG > 2
Note:
The desired quantile is specified with the following command

LET QUANT = <value>

If <value> is between 1 and 100, it is interpreted as as percentile (i.e., the quantile will be determined by dividing by 100). If <value> is between 0.5 and 1, then 1 - <value> will be used. If <value> is less than or equal to 0 or greater than or equal to 100, an error message will be printed.

Note:
Dataplot statistics can be used in a number of commands. For details, enter

Default:
None
Synonyms:
QQUANTILE RANGE is a synonym for Q QUANTILE RANGE.
Related Commands:
 INTERQUARTILE RANGE = Compute the interquartile range of a variable. RANGE = Compute the range of a variable. QUANTILE = Compute a specified quantile of a variable. STANDARD DEVIATION = Compute the standard deviation of a variable. AVERAGE ABSOLUTE DEVIATION = Compute the average absolute deviation of a variable. MEDIAN ABSOLUTE DEVIATION = Compute the median absolute deviation of a variable.
Reference:
Rand Wilcox (1997), "Introduction to Robust Estimations and Hypothesis Testing," Academic Press, pp. 24-25.
Applications:
Robust Data Analysis
Implementation Date:
2012/9
Program 1:
```LET Y1 = LOGISTIC RANDOM NUMBERS FOR I = 1 1 1000
LET Y2 = DOUBLE EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 1000
LET Y3 = NORMAL RANDOM NUMBERS FOR I = 1 1 1000
LET QUANT = 0.10
LET A1 = Q QUANTILE RANGE Y1
LET A2 = Q QUANTILE RANGE Y2
LET A3 = Q QUANTILE RANGE Y3
PRINT A1 A2 A3
```
The following output is generated.
``` PARAMETERS AND CONSTANTS--

A1      --         4.1971
A2      --         3.1889
A3      --         2.4609
```
Program 2:
```
SKIP 25
TITLE AUTOMATIC
TITLE CASE ASIS
XLIMITS 1 10
MAJOR XTIC MARK NUMBER 10
MINOR XTIC MARK NUMBER 0
XTIC OFFSET 1 1
X1LABEL BATCH
X2LABEL Q = 0.20
Y1LABEL Q QUANTILE RANGE OF DIAMETER
CHARACTER CIRCLE
CHARACTER FILL ON
CHARACTER HW 2 1.5
LINE BLANK
LET QUANT = 0.20
Q QUANTILE RANGE PLOT DIAMETER BATCH ```

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Date created: 09/07/2012
Last updated: 10/07/2016